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Theorem iunxdif2 4378
 Description: Indexed union with a class difference as its index. (Contributed by NM, 10-Dec-2004.)
Hypothesis
Ref Expression
iunxdif2.1
Assertion
Ref Expression
iunxdif2
Distinct variable groups:   ,,   ,,   ,   ,

Proof of Theorem iunxdif2
StepHypRef Expression
1 iunss2 4375 . . 3
2 difss 3630 . . . . 5
3 iunss1 4342 . . . . 5
42, 3ax-mp 5 . . . 4
5 iunxdif2.1 . . . . 5
65cbviunv 4369 . . . 4
74, 6sseqtr4i 3536 . . 3
81, 7jctil 537 . 2
9 eqss 3518 . 2
108, 9sylibr 212 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  A.wral 2807  E.wrex 2808  \cdif 3472  C_wss 3475  U_ciun 4330 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-iun 4332
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